The Polymer Basis of Kinetics and Equilibria of Enzymes: The Accessible-Volume Origin of Entropy Changes in a Class Aβ-Lactamase

Abstract

The occurrence of enzymatic catalysis, as for any chemical reaction, depends critically upon close contact of the reactants, since making/breaking of bonds occurs over distances of about 0.2 Å. Unlike small molecules, each enzyme molecule acts as an ordered solvent and reactant. Each group important to the enzyme reaction interacts with the substrate, then moves away, and subsequently binds another substrate. In other words, the group undergoes round trips in structure. For a round trip, the thermochemical state functions ΔG, ΔH, ΔS, etc., are zero. As a consequence, control of the binding of substrate must reside in the nonbinding conformations of the polymer since they govern the different fractions of time the macromolecule is in the correct conformation for bonding. Applying standard macromolecular models to the enzymes suggests that the majority of free energy for an enzyme reaction resides in the enzyme structure as an entropic contribution. Enthalpic contributions come from bond formation with the substrates and substrate structural changes. Further, it is shown that the molecular mechanisms that can effect binding and allosteric control fall into only three classes. Three x-ray structures of class A β-lactamases (native, mutant, and with substrate) show the individual binding groups at the active site change their accessible volumes depending on substrate binding and mutant form. From these volume differences, the ΔS of reaction is calculated. The x-ray-derived ΔG = −TΔS matches the ΔG = −RT ln k₁ from changes in rate constants for the same set of β-penicillinases.